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.