Earthquake in my mind!

Algebra Level 3

$\big(a^8 + b^8 + c^8 + d^8 + e^8\big)\big(a^{11} + b^{11} + c^{11} + d^{11} + e^{11}\big)$

If $a, b, c, d, e$ are the roots of $x^5 + 7x - 1 = 0,$ then find the value of the expression above.