Let $S$ be the set of ordered triples $(x,y,z)$ of real numbers for which ${\log }_{10}(x+y)=z$ and ${\log }_{10}(x^2+y^2)=z-1$. There are real numbers $a$ and $b$ such that for all ordered triples $(x,y,z)$ in $S$ we have $x^3+y^3=a\cdot 10^{3z}+b\cdot 10^{2z}$. What is the value of $a+b$?