Start with the hint you were given: Restate the complex number "z" in it's generic "a + bi" form. Use this to create an expression for the conjugate of "z". Use what you've learned about multiplying polynomial expressions to find the expression for the cube of "z". Combine and simplify as much as you can.
Then note that you have "(real number) + (other real number)*i = 0 + 0i". Equate the parts, creating two equations in "a" and "b". Solve to find the value(s) of "z".
If you get stuck, please reply showing all of your work, starting with your expression (in terms of "a" and "b") for the conjugate of "z". (Or, if you know nothing about complex numbers, conjugates, etc, please specify such, so we can try to find some online lesson links for you). Thank you!