An algebra problem by avn bha

1 ( x 1 ) ( x 2 ) + 1 ( x 2 ) ( x 3 ) + 1 ( x 3 ) ( x 4 ) = 1 6 \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 x x that satisfy the above equation?

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