Algebra Level 5

Find the sum of all positive integers $$n,k_1, k_2, \ldots , k_n$$ such that $$\displaystyle \sum_{m=1}^n k_m = 5n - 4$$ and $$\displaystyle \sum_{m=1}^n \dfrac1{k_m} = 1$$.

Note: The order of $$k_i$$ do not matter.

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