Pestañeishon

Algebra Level 4

Let \( x\ge y\) be real numbers such that:

\[\large (2x+2y-1) (x+y ) -6xy=-\frac { 1 }{ 2 } \]

The sum of all possible different values of \(x\) is \(\dfrac { a }{ b } \), with \(a\) and \(b\) are coprime positive integers. Compute \(a+b\).

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