f(x) = x⁵ + 5x⁴ + 5x³ + 5x² + 1
g(x) = x⁵ + 5x⁴ + 3x³ - 5x² -1

For the above two functions find the sum of all prime numbers p for which there exists a natural number 0 <= x < p such that both f(x) and g(x) are divisible by p.