Not sick of basick - 2

Algebra Level 5

Let \(p(x)\) be a fourth degree polynomial such that \(p(1)=1\), \(p(2)=\frac{1}{2}\), \(p(3)=\frac{1}{3}\), \(p(4)=\frac{1}{4}\), \(p(5)=\frac{1}{5}\) and \(p(6)=\frac{A}{B}\).

Find \(A+B\), where \(A\) and \(B\) are coprime.

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