Final answer:
The British Invasion was the international music that most significantly influenced American music during the 1960s, with bands like The Beatles leading the cultural and musical wave.
Step-by-step explanation:
The international music that influenced music in the United States the most during the 1960s was the British Invasion. This term is used to describe the influx of British bands like The Beatles, The Rolling Stones, and The Who which dominated American music charts and indeed, the entire American music scene during the decade.
The Beatles, in particular, became a cultural sensation influencing fashion, language, and attitudes, as well as music. Although other genres like Country and Western, Acid Rock, and Motown were also influential, the British Invasion had a monumental impact in reshaping American music, bringing with it a new wave of rock 'n' roll that would eventually merge with other forms and contribute to the development of new genres like psychedelic rock.