Too many points!

Geometry Level 3

Alice has an equilateral triangle \(ABC\) of area 1. Put \(D\) on \(BC,\) \(E\) on \(CA,\) and \(F\) on \(AB,\) with \(BD = DC, CE = 2EA,\) and \(2AF = F B.\) Note that \(AD, BE,\) and \(CF\) pass through a single point \(M.\)

If the area of the triangle \(EMC\) can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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