I'm about 5'6 and I weigh 168 pounds. But I don't look heavy at all. And I've just been wondering how I can lose maybe 20-30 pounds in a month or so. Yes I know it's a lot and I know if I can do it, it might not be the healthiest. What if I were to eat only vegetables, fruit, and lean meat for a month and do a cardio exercise for 50 minutes everyday? I haven't really been eating all that much...

That's a good start, but it won't lose the amount you are looking for.
This goal is a little on the extreme side, but a change of diet and exercise will help a great deal.