Let \( f \) be a twice differentiable function on \( \mathbb{R} \). If \( f'(0) = 4 \) and \( f(x) + \displaystyle\int\limits_{0}^{x} (x-t) f'(t) \, dt = (e^{2x} + e^{-2x}) \cos 2x + \dfrac{2}{a} x \), then \( (2a+1)^5 a^2 \) is equal to ____________ .
