Problem 24 (2019 AMC 10A)

Let $p$, $q$, and $r$ be the distinct roots of the polynomial $x^3 - 22x^2 + 80x - 67$. It is given that there exist real numbers $A$, $B$, and $C$ such that $\frac{1}{s^3 - 22s^2 + 80s - 67} = \frac{A}{s-p} + \frac{B}{s-q} + \frac{C}{s-r}$ for all $s \notin \{p, q, r\}$. What is $\dfrac{1}{A} + \dfrac{1}{B} + \dfrac{1}{C}$?