\[ \large \int_1^3 \dfrac{ \ln(x+1)}{x^2} \, dx \]

If the value of the integral above is in the form of \( \ln \left( \dfrac a {b^{c/d}} \right) \), where \(a,b,c\) and \(d\) are positive integers with \(b\) minimized and \(c,d\) coprime, find \(a+b+c+d\).

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