2007 AMC 12A 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\qquad \mathrm{(B)}\ 9\qquad \mathrm{(C)}\ 19\qquad \mathrm{(D)}\ 24\qquad \mathrm{(E)}\ 26

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.