2013 Cayley Problem 18

A two-digit positive integer x has the property that when 109 is divided by x, the remainder is 4. What is the sum of all such two-digit positive integers x?

\textbf{(A)}\ 36\quad \textbf{(B)}\ 56\quad \textbf{(C)}\ 50\quad \textbf{(D)}\ 71\quad \textbf{(E)}\ 35

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.