Let $a, b, c$ be the roots of the equation $x^3 - 9x^2 + 11x - 1 = 0$, and define $s = \sqrt{a} + \sqrt{b} + \sqrt{c}$. Compute $s^4 - 18s^2 - 8s$.

Let's think step by step and output the final answer within \boxed{}.
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