Commercial Fixed Wing
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Flight Crew Last 90 Days 200; Flight Crew Type 11000
Troubleshooting; Human-Machine Interface; Situational Awareness; Communication Breakdown; Confusion
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Environment - Non Weather Related; Human Factors
Denver Center cleared us direct to MITBEE (MMB); but we heard MNKEE instead.  Both fixes were on our route.  Since we didn't know that MMB was MITBEE until much later in the flight; we assumed the clearance was direct MNKEE.  We read back 'cleared direct MNKEE' to Denver Center and then programmed the LNAV direct and executed that clearance.  Later in the flight; ATC asked us which fix we were flying to and we said MNKEE.  The Controller and I figured out that we had previously been cleared to MITBEE; but had mistakenly proceeded to MNKEE.   Both fixes were on our route and sounded similar.  We repeated the wrong fix and our error was not noticed by ATC.  This type of error is very difficult to catch.  Crew vigilance and situational awareness must be maintained to try to trap such errors.  ATC could have told us 'cleared direct MITBEE; Mike Mike Bravo' and that might have prevented our mistake.
[Report narrative contained no additional information.]
Air carrier flight crew reported after Denver Center issued a clearance to a fix; the flight crew proceeded to a similar sounding fix. ATC informed the flight crew later that they were proceeding to the wrong fix.