AMC 12 2020a Problem 15

In the complex plane, let $A$ be the set of solutions to $z^3 - 8 = 0$ and let $B$ be the set of solutions to $z^3 - 8z^2 - 8z + 64 = 0$. What is the greatest distance between a point of $A$ and a point of $B?$

$\textbf{(A) } 2\sqrt{3} \textbf{(B) } 6 \textbf{(C) } 9 \textbf{(D) } 2\sqrt{21} \textbf{(E) } 9 + \sqrt{3}$