Yes, you should amend the Federal return to include the income that you missed.
As for State ... I don't know. The net amount on your existing Minnesota return is correct, but Minnesota starts with some of the Federal numbers, so Minnesota will likely see your amended Federal return and want to change your State return. The Minnesota return SHOULD show the Federal amount (including the Frontline pay), then it subtracts it out separately (line 29 of Form M1M).
