2004 Dodge Dakota Noise from the front end.

I have a 2004 Dodge Dakota, 124000 miles. When driving the car, there is a vibration and a sound coming from the front end. When I turn right at a high enough speed, the sound and vibration goes away. When I turn left, the sound and vibration stays. I have had a mechanic look at everything and my tires seem to be the only problem. They are worn. But, I have put the spare on both sides and the problem remains. The wheel hubs are brand new, and nothing else seems to be wrong.