Given four reals \((a,b,c,d)\). If \( \dfrac{(a-b)(c-d)}{(b-c)(d-a)} = -\dfrac{4}{7} \), then the value of \( \dfrac{(a-c)(b-d)}{(a-b)(c-d)} = \dfrac{A}{B} \), where \(A,\) and \(B\) are coprime positive integer. If the value of \( \dfrac{A+B}{A-B} = \dfrac{C}{D} \), where \(C,\) and \(D\) are coprime positive integer, find \( A+B+C+D\).

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