Given that the integers \(a, b\) satisfy the equation \[\left[\frac{\frac{1}{a}}{\frac{1}{a}-\frac{1}{b}}-\frac{\frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}\right]\left({\frac{1}{a}-\frac{1}{b}}\right)\cdot\frac{1}{\frac{1}{a^2}+\frac{1}{b^2}}=\frac{2}{3},\]find the value of \(a+b.\)