What's C, G, and N?

Let $C$ be the answer to this problem .
Let $G$ be the answer to this problem .
Let $N$ be the answer to this problem .

Let $m$ be the largest root of $x^3 + Cx^2 + Gx - N = 0$ . $m$ can be written as $\sqrt{a} - \sqrt{b}$ , where $a,b$ are positive integers. What is the value of $a+b$ ?