Summing Extremena

Algebra Level 5

Let \(f(x)=x^2-2ax-a^2-3/4\). Let \(X\) be the sum of the largest and smallest \(a\) for which \(|f(x)| \leq 1\) for all \(x \in [0, 1]\). If \(X\) can be expressed as \(\dfrac{\sqrt{n}-m}{p}\), then find \(m+n+p\).

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