An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies $75\%$ of the volume of the frozen ice cream. What is the ratio of the cone's height to its radius? Provide your answer in the form $x:1$, where $x$ is a positive integer. Please find the value of $x$.

Let's think step by step and output the final answer within \boxed{}.
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