Question $5$: Shortest Paths and Negative Edges.

We discussed in class that Dijkstra's algorithm requires all the edge weights to be non$-$negative in order to work. A student suggests a simple fix. Given a graph $\backslash ($ G $\backslash )$ with some negative weight edges, he suggests computing the least weight $\backslash ($ w$\_\{\backslash$min $\}\backslash )($which will be negative$),$ and then adding $\backslash (\backslash$left$|$w$\_\{\backslash$min $\}\backslash$right$|\backslash )$ to all the edge weights. This would make all the weights non$-$negative. He claims that the shortest path in this new graph also yields the shortest path in $\backslash ($ G $\backslash )("$because the weights are just shifted", he says..$).$

Is there something wrong in the reasoning above? Explain with an example.