Let \(\theta\) be the angle formed by two vectors \(\overrightarrow{a}=(3,~-4)\) and \(\overrightarrow{b}=(15,~8)\).

Then \(\cos\theta=\dfrac{q}{p}\).

Given that \(0<\theta<\dfrac{\pi}{2}\), and \(p,~q\) are coprime integers, find the value of \(p+q\).

*This problem is a part of <Beginner Vector Geometry> series.*

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