Calculus or Algebra?

Algebra Level 3

\[f(x,y) = x^{2} + 13y^{2} - 6xy - 4y - 2\]

Let \(x\) and \(y\) be real numbers. If the minimum value of \(f(x,y) \) occurs when \((x,y) = (A,B) \), find \(A+B\).

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