Hail Stewart-1!

Geometry Level 3

In ABC\triangle ABC, AC=BCAC=BC, point DD is on BCBC such that CD=3×BDCD=3\times BD, and EE is the midpoint of ADAD such that CE=7CE=\sqrt 7 and BE=3BE=3.

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

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