（UK Emanuel School Entrance Examination Year $7$ Entry Question \#$28$）  When a number is divided by $5$ there is a remainder of $1$.  When the number is divided by $6$ there is a remainder of $1$.  But when the number divided by $11$ there is a remainder of $0$.  What is the smallest possible value of the number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Chinese Remainder Theorem with Constant Remainder