An engineer is given a fixed volume \(V_m\) of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is always pressurized to near its bursting point, the amount of gas the vessel can contain, \(n\) (measured in moles), does not depend on the radius \(r\) of the vessel. Instead, it depends only on \(V_m\) (measured in \(\text{m}^3\)), the temperature \(T\) (measured in \(\text{K}\)), the ideal gas constant \(R\) (measured in \(\text{J/(K} \cdot \text{mol})\)), and the tensile strength of the metal \(\sigma\) (measured in \(\text{N/m}^2\)). Express \(n\) in terms of these parameters. The original answer is in the form \(\frac{k}{m} \times \frac{V_m\sigma}{RTn}\). Please give the value of \(k + m + n\).

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