2023 AMC 12A Problem 10

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

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.