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

a^{2}+b^{2}+c^{2}+d^{2}=\frac{m}{n}

Find m+n.