TxO Math Bowl 2024 - Guts Contest - Set 7 Problem 2

Given

x = 3 + \cfrac{2x^2 - 1}{3 + \cfrac{2x^3 - x}{3x + 2x^2 - 1}}

the largest real solution can be written as \frac{\sqrt{a} - b}{c}, where a, b, and c are positive integers with a not divisible by the square of any prime. Compute a + b + c.