AMC 12 2007a Problem 15

The set $\{3,6,9,10\}$ is augmented by a fifth element $n$, not equal to any of the other four. The median of the resulting set is equal to its mean. What is the sum of all possible values of $n$?

$\mathrm{(A)}\ 7 \mathrm{(B)}\ 9 \mathrm{(C)}\ 19 \mathrm{(D)}\ 24 \mathrm{(E)}\ 26$