Let \( C_r \) denote the binomial coefficient of \( x^r \) in the expansion of \( (1+x)^{10} \). If for \( \alpha, \beta \in \mathbb{R} \)
\( C_1 + 3\cdot 2\, C_2 + 5\cdot 3\, C_3 + \ldots \text{ up to } 10 \text{ terms} = \dfrac{\alpha \times 2^{11}}{2^{\beta}-1}\left( C_0 + \dfrac{C_1}{2} + \dfrac{C_2}{3} + \ldots \text{ up to } 10 \text{ terms} \right) \)
then value of \( \alpha + \beta \) is equal to ______.
