AMC 8 2009 Problem 17

The positive integers $x$ and $y$ are the two smallest positive integers for which the product of $360$ and $x$ is a square and the product of $360$ and $y$ is a cube. What is the sum of $x$ and $y$? $\textbf{(A)}\ 80 \textbf{(B)}\ 85 \textbf{(C)}\ 115 \textbf{(D)}\ 165 \textbf{(E)}\ 610$