A strange equation

Algebra Level 4

Suppose aa and bb are positive numbers satisfying 1a1b=1a+b \dfrac {1}{a} - \dfrac {1}{b} = \dfrac {1}{a+b} . Determine the value of a6b6+b6a6 \dfrac {a^6}{b^6} + \dfrac {b^6} {a^6} .

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