\[ \begin{eqnarray} f(x) &=& x^5 + 5x^4 + 5x^3 + 5x^2 + 1 \\ g(x) & =& x^5 + 5x^4 + 3x^3-5x^2-1 \end{eqnarray} \]

We define the two functions as above.

Find the sum of all prime numbers \(p\) for which there exists a natural number \(0\leq x<p\), such that both \(f(x)\) and \(g(x)\) are divisible by \(p\).

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