Let $$C_r$$ denote the binomial coefficient of $$x^r$$ in the expansion of $$(1 + x)^{10}$$. If for $$\alpha, \beta \in R$$,
$$C_{1} + 3 \cdot 2C_{2} + 5 \cdot 3C_{3} + \ldots $$ upto 10 terms $$= \frac{\alpha \times 2^{11}}{2^{\beta} - 1}(C_{0} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + \ldots $$ upto 10 terms ) then the value of $$\alpha + \beta $$ is equal to ______.