x+y=1

xy=1

x^{3}+y^{3}=z

wolfram gives me x=-1^(1/3), y=1-(-1^(1/3)), and z=-2, and another set.

Not only can't I solve this problem without crutching with wolfram, there is supposed to be an easier method to solve without using systems, what is this method?

PS sorry for no latex, I'm limited to cell phone Internet until I finish moving >.<