Have to admit...this may be pretty difficult (all those "k"s). Just some hints: 1966, New Jersey, the band's only top-chart song was a complaint about someone not telling the truth...
As I said, it's an American Band (New Jersey), they had a Single Hit in 1966 (complaining about unsincerity: "----!"), and that was said to be the "...most Beatles-like song ever" (being compared to "A Hard Day's Night"!)