The angle of incidence is the angle between the chord of the wing and the longitudinal axis of the airplane. But the plane is mostly free to pitch as necessary. So if the best thing is for the wing to have an AOA of 11°, then it can pitch to that point.
Now if the angle of incidence were too different, it could increase drag on the climb-out, or the thrust angle might be less than optimal. But there's no direct relationship.
The angle of incidence is a figure about the geometry of the plane. The angle of attack is how the wing is oriented to the wind. They don't "add" together.
If you did the math the other way (AOA - AOI), you'd find the angle the wind is making with respect to the airplane axis, not a figure that you tend to need.