Triangle mix

$\triangle ABC$ 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 $m+n$ .