1. Remove your carbs, hold a rag near the intakes and spray starting fluid onto it so it enters the combustion chamber. If you get combustion on both sides, the issue is the carb and it's ability to supply fuel to BOTH cylinders. (Check too, that any intake hose barbs for the petcock are either hooked up to tubes, or closed off with rubber dummy cap or sealed section of appropriate width air or fuel hose. Like there's a nipple for the petcock vacuum hose on BOTH sides, and you need to make sure the spare one is sealed closed. If that's off the bike will fire horribly.)
2. Move spark plugs from one side to another. If you get a change, the issue is the spark plug.
3. Do the same with your coils. Label them clearly which is the correct side, see if swapping them helps...
4. Check your valves. If they are badly adjusted the problem will persist.
So if you have a cdi, do you have a trigger coil or pickup coil? I don't know how those bikes work, but I'd check that out. I fixed a triumph that had a similar issue. As the pickup coil failed, one cylinder refused to fire...
Good luck and keep us posted.
Drewcifer