Too many points!

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 $a+b$ .