Mathematics Question from JEE Main 2023 · 29 January, Shift 1

Suppose $f$ is a function satisfying $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{N}$ and $f(1) = \frac{1}{5}$. If the sum from $n = 1$ to $m$ of $\left[\frac{f(n)}{n(n + 1)(n + 2)}\right]$ equals $\frac{1}{12}$, then $m$ is equal to: