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Algebra Level 3

Find \(x\ne 0 \) that satisfies the following: \[\large \dfrac{1}{\dfrac{1}{\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{2}}+\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{2}}}+\dfrac{1}{\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{2}}+\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{2}}}} =\dfrac{x}{36}\]

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