According to Wolfram Alpha, the nine roots add up to

or with more digits:

The terms of the sum given ar apparently not aligned with the real portions of the roots. For example 5^(1/9) ~=  1.195813174500402, which is not one of the real portions below.

The approximate roots are:

x ~= 2.2090455318317256593604383

x ~= 0.26505329725893685876037583 - 0.34122374681750815905638328 i

x ~= 0.70579407090012987387086484 - 0.86405670242277285655317631 i

x ~= 1.3809564134053568235954976 - 0.9826415597437514803802414 i

x ~= 1.9746096483625113932605946 - 0.6414095447893572175372549 i

x ~= 0.26505329725893685876037583 + 0.34122374681750815905638328 i

x ~= 0.70579407090012987387086484 + 0.86405670242277285655317631 i

x ~= 1.3809564134053568235954976 + 0.9826415597437514803802414 i

x ~= 1.9746096483625113932605946 + 0.6414095447893572175372549 i

The roots appear to be on a circle centered on a point on the real axis.

https://drive.google.com/open?id=1y1gSbaduU11cSh4aY6-i2Bb2wzvxQuLP