If $f(x) = 5x - 2$, then find the value of $x$ which satisfies $f^3(x) = -20 - x$. If $x$ can be expressed as an irreducible fraction $\frac{a}{b}$, find $a+b$ assuming $a, b>0$.

Note: $f^3(x) = f(f(f(x)))$, NOT $(f(x))^3$.

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