What does a zero matter

Algebra Level 1

Two of the roots of the equation $ax^3 + bx^2 + cx + d = 0$ are $2 - \sqrt{3}$ and $5$ , where $a,b,c,d$ are rational numbers. If the third one is $m + \sqrt{n}$ for some integers $m$ and $n$ , find $m + n$