In \triangle A B C, A C=B C, and point D is on \overline{B C} so that C D=3 \cdot B D. Let E be the midpoint of \overline{A D}. Given that C E=\sqrt{7} and B E=3, the area of \triangle A B C can be expressed in the form m \sqrt{n}, where m and n are positive integers and n is not divisible by the square of any prime. Find m+n.