You are correct so far.
So you know that the maximum and minimum values of 11cos x + 3sin x are ?
Cube those.
Express 11cosx + 3sinx in the for R cos(x-y), where R and y are constants. Hence find the maximum and minimum values of (11cosx + 3sinx)^3, and the corresponding values of x where 0<x<360 [degrees].
[I calculated that R = square root of 130 while y = 15.3 degrees, do correct me if I'm wrong.] Thank you!