AMC 12 2023a Problem 10

Positive real numbers $x$ and $y$ satisfy $y^3 = x^2$ and $(y-x)^2 = 4y^2$. What is $x+y$?

\textbf{(A)}\ 12 \textbf{(B)}\ 18 \textbf{(C)}\ 24 \textbf{(D)}\ 36 \textbf{(E)}\ 42