Let $$y = y(x)$$ be the solution of the differential equation $$\left((x+2)e^{\left(\frac{y+1}{x+2}\right)} + (y+1)\right)dx = (x+2)dy$$, $$y(1) = 1$$. If the domain of $$y = y(x)$$ is an open interval $$(\alpha, \beta)$$, then $$|\alpha + \beta|$$ is equal to ___.