Let ^n C_r denote the binomial coefficient of x^r in the expansion of (1+x)^n. If Σ_k=0^10(2^2+3 k)^n C_k=α.3^10+β.2^10, α, β ∈ R, then α+β is equal…

Let $\displaystyle { }^{\mathbf{n}} \mathbf{C}_{\mathbf{r}}$ denote the binomial coefficient of $\displaystyle x^{\mathbf{r}}$ in the expansion of $\displaystyle (1+x)^{\mathbf{n}}$. If $\displaystyle \sum_{k=0}^{10}\left(2^2+3 k\right){ }^n C_k=\alpha .3^{10}+\beta .2^{10}, \alpha, \beta \in R$, then $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.