Let $$P$$ be a point in the interior of a triangle $$ABC$$ and let $$AP, BP, CP$$ meet the sides $$BC, CA, AB$$ in $$D, E, F$$ respectively. If $$ \frac{BP}{PE}=\frac{5}{2}, \frac{CP}{PF}=\frac{7}{3},$$ and $$ \frac{AP}{PD}=\frac{p}{q}, $$ where $$p$$ and $$q$$ are natural numbers and $$gcd(𝑝, 𝑞) = 1$$, find $$𝑝 + 𝑞$$.