Let point $P\left(x_1,y_1\right)$ be the point on this curve such that the tangent of $P$ passes through the origin.

Equation of tangent at $P$ is $y-y_1=\left(3x_1^2+1\right)\left(x-x_1\right)$
It passes through $\left(0,\mathrm{}0\right)$ so $y_1=\left(3x_1^2+1\right)x_1$
$\Rightarrow x_1^3+x_1+54=3x_1^3+x_1$
$\Rightarrow x_1^3=27\Rightarrow x_1=3$
So, ${\left.\frac{dy}{dx}\right|}_{\left(x_1,\mathrm{}{y}_1\right)}=3x_1^2+1=3\left(9\right)+1=28$