Doing both is definitely doable.
You can't use cuda miner though on the CPU. You'll have to use something like pool's miner. If you have a nice CPU there are some things to be cautious about.
1. You'll be running CPU and GPU at 100% more than likely which if your PSU can't support will cause it to blow.
- Games never use both at 100% so it will really stress the system
2. You'll be outputting a lot more heat. So things can get really toasty in a case.
3. You won't get much more hash/sec with cpu mining. As a benchmark I could only get around 90kh/s using an intel i7 4770k, and about the same with an i7 3930k
- So you might be using more power than it's worth.
The key question for the PSU is your 12V rail. If you can cover the TDP of the GPU and the CPU as well as wattage for memory, optical drives, and the northbridge, you'll be okay. Not all of those work off of 12V. Personally I just strip out the optical drive. The hard drive and memory take 5 to 10 watts each and the northbridge takes 20ish. So if you want a theoretical max take TDP of GPU + CPU + 40 watts (and don't have a DVD in the optical drive...).
On your PSU you can check what the 12V rail is rated. So for a 430 watt CX psu for example, the 12V rail is rated at 384 watts (32 AMPS * 12 VOLTS = 384 WATTS). You need the total internal pull on your system to be less than 384. Now really, as a bare minimum, if you want your PSU to last any sort of time, you need to be at least 10 percent under that target so (384-38=346) to cover power fluctuations and not overwork the PSU, but if you want to be safe (and you should PSUs cost money) try to be 20 percent under (384-77=307). So your total system in this case should be pulling 307 watts maximum.
Another note (although I haven't tried it myself) is that I have heard that LTC/scrypt mining needs one open core. So if you have multiple cores, try to only use N-1 (where N is the number of cores in the CPU) for the CPU coin. That way you wont weaken your LTC or scrypt return.
Happy mining.
--GarbageName