Let $\alpha,\beta$ be the distinct roots of $x^{2}-(t^{2}-5t+6)x+1=0$, $t\in\mathbb{R}$, and let $a_n=\alpha^{n}+\beta^{n}$. Then the minimum value of $\dfrac{a_{2023}+a_{2025}}{a_{2024}}$ is: