# Triangle mix

Geometry Level 3

$$\triangle ABC$$ is equilateral. Point $$P$$ is on $$AB$$ extension such that $$\dfrac{AP}{AB}=\dfrac{5}{3}$$. Point $$Q$$ is on $$BC$$ such that $$\dfrac{QB}{2}=CQ$$. The intersection of the $$AC$$ side and $$PQ$$ extension is $$R$$. The midpoint of the $$AB$$ side is $$F$$.

If the area of $$\triangle FQR$$ is 1 and the area of $$\triangle ABC$$ is $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime integers, find the value of $$m+n$$.

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