In general the given function is in the form y=f(x) and its inverse is f^(-1)(y)=x, provided that f(x) is always crescent or decrescent for each value in the domain. This is just the case, being f'(x)=5+11x^(10) always positive for any x in R.
checked this, the problem of finding f^(-1)(-13)=x can be seen in an equivalent way as the one of finding the value of x whose image is -13.
To find it, it is enough to solve the equation 8x^(11)+5x-13=0.
This has one root in x=-1 so that at this point in the domain corresponds the value y=-13 in the image. Being f(-1)=13 and verified its monotonicity, we can concude that f^(-1)(-13)=-1