CAT 2023 Linear and Quadratic Equations — Previous Year Question

A quadratic equation $x^2 + bx + c = 0$ has two real roots. If the difference between the reciprocals of the roots is $13\frac{1}{3}$, and the sum of the reciprocals of the squares of the roots is $59\frac{5}{9}$, then the largest possible value of $(b + c)$ is: