Answer. $26$ km/h.

Let the location of the Mumbo-Jumbo tribe be $O$, the raft location to which Mumbo ran be $M$, and the raft location to which Jumbo went be $U$. Obviously, $M$ is upstream from $O$, and $U$ is downstream.

Let the distances from $O$ to $M$ and $U$ be $x$ and $y$ km respectively ($x < y$), and let the river speed be $v$ km/h. The time Jumbo spent from $O$ to $U$ is $\frac{y}{6}$ hours, and Mumbo spent $\frac{x}{11} + \frac{x+y}{v}$ hours. Clearly, Jumbo arrives at the neighboring tribe earlier than Mumbo if and only if

$$\frac{y}{6} < \frac{x}{11} + \frac{x+y}{v}.$$

Since $x < y$, it follows from this inequality that

$$\frac{y}{6} < \frac{y}{11} + \frac{2y}{v}.$$

Dividing by $y$ and rearranging, we get $v < 26.4$.

It remains to check that the river speed could be $26$ km/h. For this, in the inequality $\frac{y}{6} < \frac{x}{11} + \frac{x+y}{v}$, set $v = 26$ and equivalently transform it to $\frac{y}{x} < \frac{111}{110}$. This is possible (for example, for $y = 1.12$ km, $x = 1.11$ km), which completes the solution.