6. Given that $\alpha$ and $\beta$ are the roots of the equations $\log _{3} x+x-3=0$ and $3^{x}+x-3=0$ respectively, then $\alpha+\beta=$
6. $\alpha+\beta=3$.

Hint: Use a combination of numerical and graphical methods. The roots of the equations $\log _{3} x=3-x$ and $3^{x}=3-x$ are the x-coordinates of the intersection points of the logarithmic function $y=\log _{3} x$ and the exponential function $y=3^{x}$, respectively. Since $y=\log _{3} x$ and $y=3^{x}$ are inverse functions, their graphs are symmetric with respect to the line $y=x$, making it easy to find that $\alpha+\beta=3$.