Absolutely Outrageous

Algebra Level 2

The set of solutions of the equation x1+11=x+11+1 \bigg\lvert \Big\lvert \lvert x-1 \rvert + 1 \Big\rvert - 1 \bigg\rvert = \bigg\lvert \Big\lvert \lvert x+1 \rvert - 1 \Big\rvert + 1 \bigg\rvert is a disjoint union of one or more segments. Find the sum of their lengths.

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