Example 1 Simplify:
$$
\frac{1}{\sqrt{8}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{14}}+\cdots+\frac{1}{\sqrt{6038}+\sqrt{6041}} .
$$
Solve: By observation and induction, we get the general term
$$
f(n)=\frac{1}{\sqrt{3 n+5}+\sqrt{3 n+8}} .
$$

Decomposing the general term, we get
$$
\begin{array}{l}
f(n)=\frac{\sqrt{3 n+8}-\sqrt{3 n+5}}{(\sqrt{3 n+5}+\sqrt{3 n+8})(\sqrt{3 n+8}-\sqrt{3 n+5})} \\
=\frac{1}{3}(\sqrt{3 n+8}-\sqrt{3 n+5}) .
\end{array}
$$

Substituting $n=1,2, \cdots, 2011$ into $f(n)$ and adding them up, we get
$$
\begin{array}{l}
\quad \text { Original expression }=f(1)+f(2)+\cdots+f(2011) \\
=\frac{1}{3}(\sqrt{6041}-\sqrt{8}) \\
=\frac{1}{3}(\sqrt{6041}-2 \sqrt{2}) .
\end{array}
$$