\[ \large \int_{-1/2}^0 H_ x \, dx = \dfrac ab \gamma - \dfrac cd \ln \pi \]

If the equation above holds true for positive integers \(a,b,c\) and \(d\) with \(\gcd(a,b) = \gcd(c,d) = 1 \), find \(a+b+c+d\).

**Notations**:

\(H_n\) denote the generalized harmonic number.

\(\gamma\) denotes the Euler-Mascheroni constant.

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