There are real numbers a, b, c, and d such that -20 is a root of x^{3}+a x+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.
There are real numbers a, b, c, and d such that -20 is a root of x^{3}+a x+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.