"So if I understand it correctly the (L/D) max is at the intersection
of parasitical drag and lift-induced drag. Thus, at the point which
has the minimum total amount of drag. Which is achieved at a specific
Actually, speaking in the most general terms, neither L/D max nor maximum Lift nor minimum Drag are achieved at a specific speed. The graph tying the L/D ratio to a specific airspeed is ASSUMING one specific weight, and also is ASSUMING 1-G flight. In many cases this is a perfectly reasonable assumption, but not always. Fundamentally speaking, L/D ratio and lift coefficient and drag coefficient are all functions of angle-of-attack, NOT airspeed.
However, in 1-G flight at a given weight, there's a one-to-one correlation between angle-of-attack and airspeed. Once you understand this, your confusion will vanish.
If we DO assume 1-G flight at one specific weight, then it's fine to say that variables like L/D ratio, lift coefficient, and drag coefficient are functions of angle-of-attack, or of airspeed, whichever we prefer. When presenting the information to a pilot who will be interested in the aircraft's performance in 1-G flight at some given known or assumed weight, then obviously it makes more sense to present the information in terms of airspeed, because the pilot has an airspeed indicator but not an angle-of-attack indicator. This would pertain more to L/D ratio than to lift coefficient or drag coefficient, because the L/D ratio is tied directly to something the pilot is actually interested in optimizing (the glide ratio), while the lift coefficient and drag coefficient aren't tied directly to any one parameter that the pilot cares about. (The lift coefficient is NOT a measure of the "efficiency" of the wing, as the question suggests.) Hence the reason you are seeing the L/D curve presented with airspeed along the X axis, rather than with angle-of-attack along the X axis. It's a graph that's meant to tell the pilot something he can actually use in the cockpit, while flying in the 1-g condition at some known or assumed weight.
Here's another bit of trivia to muddy the waters:
If the L/D graph is drawn for horizontal powered flight, the point of max L/D will occur exactly at the point of minimum Drag (not the same as minimum drag coefficient), because in horizontal powered flight Lift = Weight, assuming no complications from a tilted thrust line, and Lift is therefore constant.
If the L/D graph is drawn for gliding flight, the point of max L/D will occur ALMOST at the point of minimum Drag, but not exactly, because in gliding flight Lift is not constant. It is slightly less than Weight, and more so at poor glide ratios than at large glide ratios. The difference will likely be too small to notice though-- for all practical purposes the gliding L/D curve and the horizontal L/D curve are interchangeable, except in aircraft with very poor glide ratios. Therefore for all practical purposes, the L/D curve can also be viewed as a Drag curve (not the same as a drag coefficient curve) in gliding flight as well as in horizontal flight, except in aircraft with very poor glide ratios.
In both cases (gliding flight or horizontal flight) the point of max L/D will occur at the point of max (lift coefficient / drag coefficient), which will occur NEITHER at the point of max lift coefficient nor at the point of minimum drag coefficient.
(By the way, all the above statements are true regardless of whether we are putting angle-of-attack, or airspeed, along the x axis of our graph.)
Always keep in mind that Drag is not the same as drag coefficient, and Lift is not the same as lift coefficient. However the Lift/ Drag ratio is always exactly equal to the ratio of (lift coefficient / drag coefficient).