The real numbers \(x\) and \(y\) are such that \(x + \frac{2}{y} = \frac{8}{3}\), and \(y + \frac{2}{x} = 3\).

The value \(x + y\) can be expressed as \(\frac{m}{n}\) for positive coprime integers \(m\) and \(n\).

Find \(m^{2} - n^{2}\).

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