jmc

The original nine numbers, with mean 54, must have a sum of $9\cdot 54=486$. After including $u$ and $v$, we have eleven numbers now, and their sum must be $11\cdot 66=726$. Since the only new numbers in this sum are $u$ and $v$, $u+v=726-486=240$. So, the mean of $u$ and $v$ is $\frac{1}{2}(u+v)=\frac{1}{2}(240)=\boxed{120}$.