On a clock, there are two instants between $12$ noon and $1$ PM, when the hour hand and the minute hand are at right angles. The difference in minutes between these two instants is written as $a+\frac{b}{c},$ where $a, b \text{and} c$ are positive integers, with $b<c$ and $\frac{L}{c}$ in the reduced form. What is the value of $a+b+c?$