Let \(S\) be the set of non-negative integer triples \((x,y,z)\) that satisfy the equation \(x + y + z = 28\). If a triple is chosen uniformly at random from \(S\), then what is the probability that the product \(xyz\) is divisible by \(7\)?

If the probability is \(\dfrac{a}{b}\), where \(a,b\) are positive coprime integers, then enter \(a + b\) as your answer.

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