A straight line is to be drawn through a point whose coordinates are \((x,y)=(2,-1)\) as tangent to the curve \(y=x^2-5x+6\). Let the coordinates of the points where the line is tangent to the curve be \((x_1,y_1)\) and \((x_2,y_2)\).

Find \(x_1+y_1+x_2+y_2\).

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