AA batteries can supply plenty current, the question is for how long.

You need about 1.3 Watt for 30 LEDs (I’m assuming 15 mA, 3V). A rechargable AA battery has about 2.4 Wh according to Wikipedia, so 6 AA batteries will last you 2.4Wh * 6 / 1.3W = 11 hours.

I have no idea how curing works, but 1.3 Watt feels very low. That amount of power is fine for visual lighting, or for signals (turn on a TV), but energy wise it’s very little.