2013 AIME II Problem 13

In \triangle ABC, AC = BC, and point D is on \overline{BC} so that CD = 3\cdot BD. Let E be the midpoint of \overline{AD}. Given that CE = \sqrt{7} and BE = 3, the area of \triangle ABC 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.