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In △ABC\triangle ABC△ABC, AC=BCAC=BCAC=BC, point DDD is on BCBCBC such that CD=3×BDCD=3\times BDCD=3×BD, and EEE is the midpoint of ADADAD such that CE=7CE=\sqrt 7CE=7 and BE=3BE=3BE=3.
If the area of △ABC\triangle ABC△ABC is mnm\sqrt nmn, where mmm and nnn are positive integers and nnn is square-free, find m+nm+nm+n.
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