There are real numbers $a,b,c,$ and $d$ such that $-20$ is a root of $x^3+ax+b$ and $-21$ is a root of $x^3+c{x}^2+d.$ These two polynomials share a complex root $m+\sqrt{n}\cdot i,$ where $m$ and $n$ are positive integers and $i=\sqrt{-1}.$ Find $m+n.$