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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