proof writing - Sum of Binomial Coefficients?

Question: Trying to find a proof of the following equation.

For any $m,n\in \mathbb{N}^0$,

$$\sum_{k=0}^{m} \binom{n+k}{k} = \binom{n+m+1}{m}.$$

I know that Vandermonde's identity might be useful but not sure where to start.