Question 120
Suppose that there exist nonzero complex numbers $a$, $b$, $c$, and $d$ such that $k$ is a root of both the equations $a x^{3} + b x^{2} + c x + d = 0$ and $b x^{3} + c x^{2} + d x + a = 0$. Find all possible values of $k$ (including complex values).