Suppose f is a function satisfying f(x+y)=f(x)+f(y) for all x, y ∈ N and f(1)=1/5. If Σ_n=1^m (f(n))/(n(n+1)(n+2))=1/12, then m is equal to ____.

Suppose $\displaystyle f$ is a function satisfying $\displaystyle f(x+y)=f(x)+f(y)$ for all $\displaystyle x, y \in \mathbb{N}$ and $\displaystyle f(1)=\frac{1}{5}$. If $\displaystyle \sum_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}$, then $\displaystyle m$ is equal to $\displaystyle \_\_\_\_$.