jmc

Let's play with the given condition a little. Clearing out the denominator gives $4a+3b=5(a-2b)=5a-10b$. Selectively combine like terms by adding $9b-4a$ to both sides to get $12b=a-b$. This gives $\frac{12b}{a-b}=1$.

Now, we want to find $\frac{a+11b}{a-b}$. Rewrite this as $\frac{a-b+12b}{a-b}=\frac{a-b}{a-b}+\frac{12b}{a-b}=1+1=\boxed{2}$, and we are done.