AMC 12 2015b Problem 11

The line $12x+5y=60$ forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?

\textbf{(A)} 20 \textbf{(B)} \dfrac{360}{17} \textbf{(C)} \dfrac{107}{5} \textbf{(D)} \dfrac{43}{2} \textbf{(E)} \dfrac{281}{13}