AMC 12 2004b Problem 11

All the students in an algebra class took a $100$-point test. Five students scored $100$, each student scored at least $60$, and the mean score was $76$. What is the smallest possible number of students in the class?

$\mathrm{(A)}\ 10 \mathrm{(B)}\ 11 \mathrm{(C)}\ 12 \mathrm{(D)}\ 13 \mathrm{(E)}\ 14$