2021 AIME II Problem 7

Let a, b, c, and d be real numbers that satisfy the system of equations

\begin{aligned} a+b & =-3 \\ a b+b c+c a & =-4 \\ a b c+b c d+c d a+d a b & =14 \\ a b c d & =30 \end{aligned}

There exist relatively prime positive integers m and n such that


Find m+n.