Will it even end?

Algebra Level 4

\[\dfrac{1}{x-1}-\dfrac{4}{x-2}+\dfrac{4}{x-3}-\dfrac{1}{x-4} < \dfrac{1}{30}\]

If the range of \(x\) satisfying the above inequality is in the form as given below.

\[(-\infty,a)\cup (b,c)\cup (d,e) \cup (f,g) \cup (h,\infty)\]

Find \(a+b+c+d+e+f+g+h\).

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