Let $f:R\to R$ and $g:R\to R$ be defined as $f\left(x\right)=\left\{\begin{array}{cl}x+a,& x<0\\ |x-1|,& x\ge 0\end{array}\right.$ and $g\left(x\right)=\left\{\begin{array}{cc}x+1,& x<0\\ (x-1{)}^2+b,& x\ge 0\end{array}\right.$, where $a, b$ are non-negative real numbers. If $gof\left(x\right)$ is continuous for all $x\in R,$ then $a+b$ is equal to ______ .