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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