jmc

Adding $3n+11$ to both sides, we get $$-3n+3+3n+11>-11+3n+11,$$ which simplifies to $$14>3n.$$ Dividing both sides by $3$ gives $$4\frac{2}{3}>n.$$ The integer solutions are $n=1,2,3,4$, and their sum is $\boxed{10}$.