If the cubic polynomial whose roots are $\cos \left( \dfrac{2\pi}7 \right),\cos \left( \dfrac{4\pi}7 \right)$ and $\cos \left( \dfrac{6\pi}7 \right)$ is of the form $a^b x^3 + a^c x^2 - a^d x - 1 \; ,$ where $a,b,c$ and $d$ are primes, find $a+b+c+d$.

**Hint**:

${z^{2n+1}-1 =(z-1) \cdot \prod_{k=1}^{n}\left(z^{2}-2 \cdot \cos \dfrac{2\pi k}{2n+1}z +1 \right) }$

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