Could be 11th Infantry Regiment (Regular Army) or - inasmuch as McClellan was an Infantry Training Facility - 11th Infantry Training Regiment or 11th Infantry Training Battalion. Assuming you've provided all the info you have, it's just not enough.
I'm going to try a long shot. If it works out, it will probably involve a fee but not that much. I'll let you know if I locate anything. In the meantime, you go through the Social Security Death Index to see if you can find a date of birth, death and/or SSN. Fair enough?