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$\alpha, \beta > 0$.

With $\alpha, \beta > 0$, if $\alpha + \dfrac{1}{\alpha}$ and $2 - \beta - \dfrac{1}{\beta}$ are the roots of the quadratic equation

$x^{2} -2(a+1)x + a - 3 = 0,$

then find the sum of integral values of $a$.

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