$\cos\left(\dfrac{2\pi}{13}\right)\cos\left(\dfrac{6\pi}{13}\right)+\cos\left(\dfrac{2\pi}{13}\right)\cos\left(\dfrac{8\pi}{13}\right)+\cos\left(\dfrac{6\pi}{13}\right)\cos\left(\dfrac{8\pi}{13}\right)$

If the trigonometric expression above can be expressed as $-\dfrac{\alpha}{\beta}$ for coprime positive integers $\alpha$ and $\beta$, find the value of $\alpha+\beta$.

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