At the beginning of the school year, $60\%$ of all students in Ms. Chang's science class answered "Agree" to the statement "Science is fascinating", and $40\%$ answered "Disagree." At the end of the school year, $45\%$ answered "Agree" and $55\%$ answered "Disagree." Altogether, $x\%$ of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of $x$?