I need help finding the anti-derivative of this function:

f(x) = the cubed root of x + 5/x^6

When I try to do the problem it comes out wrong:

f(x) = x^1/3 + 5(x^-6)

f(x) = x^(1 + 1/3)/1 + 1/3 + 5([x^(1 - 6)]/1 - 6)

f(x) = x^4/3/4/3 + 5([X^-5]/-5)

f(x) (4/3)x^4/3 - x^-5

Someone please help.