jmc

The equation can be rewritten as $\lceil \frac{3}{2}\rceil +\lceil \frac{9}{4}\rceil +\lceil \frac{81}{16}\rceil$. The smallest integer greater than $\frac{3}{2}$ is $2$. The smallest integer greater than $\frac{9}{4}$ is $3$. The smallest integer greater than $\frac{81}{16}$ is $6$. Therefore $2+3+6=\boxed{11}$.