A number theory problem by Aquilino Madeira

Find the integer nn satisfying (n+1)!3(n1)!(n+1)!+3(n1)!=5359\dfrac{{(n + 1)!\, - 3(n - 1)!}}{{(n + 1)!\, + 3(n - 1)!}} = \dfrac{{53}}{{59}} .

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