Given that $\dfrac{\sin x}{\sin y} = 3$ and $\dfrac{\cos x}{\cos y} = \dfrac{1}{2}$.

The value of $\dfrac{\sin2x}{\sin2y}- \dfrac{\cos2x}{\cos2y}$ can be expressed as $\dfrac{p}{q}$ for coprime positive integers $p$ and $q$. Find $p+q$.

This is a modified AIME problem.

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