Let the current age of Mr. X be 'a'. Last year, his age was 'a-1', which was a perfect square (n^2). Next year, his age will be 'a+1', which is a perfect cube (m^3). Thus, m^3 - n^2 = 2. The only integer solution for this is m=3 and n=5, which gives 3^3 - 5^2 = 27 - 25 = 2. So, last year's age was 25 (5^2), making the current age 26, and next year's age 27 (3^3). We need to find the smallest waiting period from the current age (26) for the age to become a perfect cube again. The next perfect cube after 27 is 64 (4^3). To reach 64 from 26, Mr. X must wait 64 - 26 = 38 years.