If the line, 2 x-y+3=0 is at a distance 1/(√ 5) and 2/(√ 5) from the lines 4 x-2 y+α=0 and 6 x-3 y+β=0, respectively, then the sum of all possible…

If the line, $\displaystyle 2 x-y+3=0$ is at a distance $\displaystyle \frac{1}{\sqrt{5}}$ and $\displaystyle \frac{2}{\sqrt{5}}$ from the lines $\displaystyle 4 x-2 y+\alpha=0$ and $\displaystyle 6 x-3 y+\beta=0$, respectively, then the sum of all possible values of $\displaystyle \alpha$ and $\displaystyle \beta$ is \_\_\_\_.