Let A B C D E be a pentagon inscribed in a circle such that A B=C D=3, B C=D E=10, and A E=14. The sum of the lengths of all diagonals of A B C D E is equal to \dfrac{m}{n}, where m and n are relatively prime positive integers. What is m+n ?
Answer Choices
A. 129
B. 247
C. 353
D. 391
E. 421