An algebra problem by avn bha

Algebra Level 3

1(x1)(x2)+1(x2)(x3)+1(x3)(x4)=16 \frac{1}{(x-1)(x-2)} + \frac{1}{(x-2)(x-3)} + \frac{1}{(x-3)(x-4)} = \frac{1}{6}

What is the sum of all real values of xx that satisfy the above equation?

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