Let \(x^5 - x^2 - x - 1 = p_1(x) p_2(x) \dotsm p_k(x),\) where each non-constant polynomial \(p_i(x)\)is monic with integer coefficients, and cannot be factored further over the integers. Compute \(p_1(2) + p_2(2) + \dots + p_k(2).\)
$p_1(2) + p_2(2) + \dots + p_k(2) = 18$
