In \triangle A B C medians \overline{A D} and \overline{B E} intersect at G and \triangle A G E is equilateral. Then \cos (C) can be written as \dfrac{m \sqrt{p}}{n}, where m and n are relatively prime positive integers and p is a positive integer not divisible by the square of any prime. What is m+n+p ?
Answer Choices
A. 44
B. 48
C. 52
D. 56
E. 60