Let ABCDE be a pentagon inscribed in a circle such that AB=CD=3, BC=DE=10, and AE=14. The sum of the lengths of all diagonals of ABCDE is equal to nm, where m and n are relatively prime positive integers. What is m+n?
<spanclass=′latex−bold′>(A)</span>129<spanclass=′latex−bold′>(B)</span>247<spanclass=′latex−bold′>(C)</span>353<spanclass=′latex−bold′>(D)</span>391<spanclass=′latex−bold′>(E)</span>421