HELP! Front end shakes when accelerating (sometimes)

We have a 1998 Mazda Millennia L 6 cly (non-turbo)with 83K miles. Recently it began… when ‘cruising’ on a highway, or long road, (occasionally) when we come to any incline, or rise in the road (as you would if you were driving to a higher altitude) and have to depress the gas petal slightly to adjust for more rpm’s, the front end will shake and vibrate. When the gas pedal is released it stops immediately and the car runs smooth as glass. It does not happen all the time - and of course NEVER, when we are anywhere near our mechanic. It has brand new Michelin tires - and all the wheel components have been checked (ball joint’s tie rods, axles, bearings, etc. HELP!

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