Hail Stewart-1!

Geometry Level 3

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 $m+n$.

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