Hail Stewart-1!

Geometry

In $\triangle ABC$ , $AC=BC$ , point $D$ is on $BC$ such that $CD=3\times BD$ , and $E$ is the midpoint of $AD$ such that $CE=\sqrt 7$ and $BE=3$ .

If the area of $\triangle ABC$ is $m\sqrt n$ , where $m$ and $n$ are positive integers and $n$ is square-free, find $m+n$ .