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