For every real number $x$, let $\lfloor x \rfloor$ denote the greatest integer not exceeding $x$, and let:
\[f(x) = \lfloor x \rfloor (2014^{x-\lfloor x \rfloor} - 1).\]
The set of all numbers $x$ such that $1 \leq x < 2014$ and $f(x) \leq 1$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?

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