AMC 12 2003b Problem 18

Let $x$ and $y$ be positive integers such that $7x^5 = 11y^{13}.$ The minimum possible value of $x$ has a prime factorization $a^cb^d.$ What is $a + b + c + d$?

\textbf{(A)}\ 30 \textbf{(B)}\ 31 \textbf{(C)}\ 32 \textbf{(D)}\ 33 \textbf{(E)}\ 34