"We think that life is going to go according to our plan," Ness wrote in an Instagram post Wednesday, "but it has a way of saying 'I don't think so!'"
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The stage 1 diagnosis was made while the band was in the midst of pre-production for a new album, Ness said.
"I was feeling well enough to continue with recording in the studio up until the very day before surgery," the singer-guitarist added. "The band and I were so inspired and excited to lay down these tracks, which by the way sound ... AWESOME!"
According to ness, the recovery from surgery is a day-by-day process "and in three weeks we start radiation and that should be the last therapy I need."
He and his doctors "expect a full recovery enabling me to live a long and productive life."
Ness said he was heartbroken to postpone the band's previously scheduled summer tour and the album's release.
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"I can't thank our loyal fans enough who have been waiting so patiently for this," he said. "While it will take a little longer-I promise you that it will be delivered and it will exceed your expectations."