Most USA bound flights from Asia enjoy a lovely and strong tail-wind, so your flight will probably be early (not too early, but early).
China Eastern (MU) arrives at TBIT (the main international terminal). Assuming your a US citizen, the line at Immigration will probably take at most 20 minutes and the Baggage claim it will take at most 30 minutes and customs (if you delcare nothing) at most 5 minutes. Walking from arrivals to UA's Terminal 7/6 (with a bus) takes 15 minutes at most if the bus is not there. Security at UA's terminal can be at most 30 minutes (if Elite (2P higher or Business/First), 5 minutes). From security to gate, give your selft at least 15 minutes (depends which terminal and which side of the terminal).
In conclusion, at very liberal estimate, give your self 90 minutes or more. But if you are an elite and deplane earlier, 70 minutes will be fine, even an hour will do.
Please do not soley rely on this advice!

Hope you enjoy your flight!
Enjoy your flight on UA.

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3 V-CLASS OP-UPGRADES! that is what i call the Friendly Skies.