The functions $f$ and $g$ are defined as $f(x)=x^2-5x+6$ and $g(x)=-x+1$. If the function $h$ is defined as $h(x)=f(x)+g(x)$, what is the sum of the $x$-coordinates of the $x$-intercepts of the graph of $y=h(x)$ in the $xy$-plane?