This can be done as MIDCP
RobPratt provides a general formulation at https://math.stackexchange.com/questions/3961000/decision-variable-must-lie-in-union-of-multiple-disjoint-intervals/3961273
In your example,
variable x
variable z(2) binary
10*z(2) <= x <= z(1) + 11*z(2)
sum(z) == 1
Note: I corrected a typo in the statement which is now variable z(2) binary