Triangle A B C has A B=13, B C=14, and A C=15. The points D, E, and F are the midpoints of \overline{A B}, \overline{B C}, and \overline{A C} respectively. Let X \neq E be the intersection of the circumcircles of \triangle B D E and \triangle C E F. What is X A+X B+ X C ?
Answer Choices
A. 24
B. 14 \sqrt{3}
C. \dfrac{195}{8}
D. \dfrac{129 \sqrt{7}}{14}
E. \dfrac{69 \sqrt{2}}{4}