Great Mathematics Olympiad problem!

All pairs $(a. b)$ of positive integers such that $a{b}^{2} + b + 7$ divides ${a}^{2}b+ a + b$ are given by
$(p, q)$ ; $(s, t)$ and $(\alpha, \beta)$ .

Find the value of $p + q + s + t$ .

Here, $\alpha, \beta$ varies over a variable for example it can be $(4{ a }^{ 2 }, 5a)$ for some variable $a$ .

And $p, q, s, t$ are natural numbers.