Holiday Contest 2025 - Team Round - Problem 11

Denote \{x\} as the fractional part of x. For example, \{1.25\} = 0.25 and \{-6.9\} = 0.1. The sum of all values of x that satisfy

20x^2 = (x - \{x\})(19x+30\{x\})

can be written as \frac{p}{q} for relatively prime positive integers p and q. Compute p+q.