Question 91
Let $f(x) = x^{3} + 3x - 1$ have roots $a, b, c$. Given that
$$
\frac{1}{a^{3} + b^{3}} + \frac{1}{b^{3} + c^{3}} + \frac{1}{c^{3} + a^{3}}
$$
can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n) = 1$, find $100m + n$.
$$
\frac{1}{a^{3} + b^{3}} + \frac{1}{b^{3} + c^{3}} + \frac{1}{c^{3} + a^{3}}
$$
can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n) = 1$, find $100m + n$.