A common tangent \( T \) to the curves \( C_{1}:\ \dfrac{x^{2}}{4}+\dfrac{y^{2}}{9}=1 \) and \( C_{2}:\ \dfrac{x^{2}}{42}-\dfrac{y^{2}}{143}=1 \) does not pass through the fourth quadrant. If \( T \) touches \( C_{1} \) at \( (x_{1},y_{1}) \) and \( C_{2} \) at \( (x_{2},y_{2}) \), then \( |2x_{1}+x_{2}| \) is equal to ______.
