Use the method for solving homogeneous equations to solve the following differential equation.

$\frac{dx}{dt}=\frac{6x^2+5t\sqrt[\phantom{2}]{5t^2+x^2}}{6tx}$

Express the equation in the form $\frac{dx}{dt}=F(\frac{x}{t}).$

$F(\frac{x}{t})=$

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