Let $\mathrm{P}\left(\dfrac{2\sqrt{3}}{\sqrt{7}}, \dfrac{6}{\sqrt{7}}\right), \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ be four points on the ellipse $9x^{2}+4y^{2}=36$. Let $\mathrm{PQ}$ and $\mathrm{RS}$ be mutually perpendicular and pass through the origin. If $\dfrac{1}{(PQ)^{2}}+\dfrac{1}{(RS)^{2}}=\dfrac{p}{q}$, where $p$ and $q$ are coprime, then $p+q$ is equal to: