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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