Increasing the weights of all edges in an undirected graph makes a minimum cut still minimum
Consider the following graph. The min-cut is $[s][a,b,c,d,t]$ with value 3. After the weights of all edges are increased by 1, the min-cut becomes $[s,a,b,c,d][t]$ with value 5. 



It does not matter whether you are considering cuts with terminals or without terminals (if with terminals, the terminals are $s$ and $t$).