jmc

Rearranging the second equation, we have that $b^3=\frac{4}{27}a$. If we substitute this into the original equation, we get $\frac{4}{27}{a}^3=\frac{32}{27}$; after multiplying each side by $\frac{27}{4}$ and taking the cube root, we see that $a=2$. Substituting $a$ into the first equation, we get that $b^3=\frac{8}{27}$ or $b=\frac{2}{3}$. Thus, $a+b=2+\frac{2}{3}=\boxed{\frac{8}{3}}$.