x3 - 1.1 = 0 has root 1.0322801154... by Intermediate Value Theorem
Below the function values f(x) = x3 - 1.1 are coloured red if negative and green if positive. x values are in black. "drop" means that endpoint is dropped at the next iteration. Data is displayed to 8 decimals but was computed to 20.

IterationLeft endpointMid pointRight endpoint
1 0.00000000   drop
-1.10000000		 1.00000000
-0.10000000		 2.00000000
6.90000000
2 1.00000000
-0.10000000		 1.50000000
2.27500000		 2.00000000   drop
6.90000000
3 1.00000000
-0.10000000		 1.25000000
0.85312500		 1.50000000   drop
2.27500000
4 1.00000000
-0.10000000		 1.12500000
0.32382812		 1.25000000   drop
0.85312500
5 1.00000000
-0.10000000		 1.06250000
0.09946289		 1.12500000   drop
0.32382812
6 1.00000000   drop
-0.10000000		 1.03125000
-0.00328979		 1.06250000
0.09946289
7 1.03125000
-0.00328979		 1.04687500
0.04731979		 1.06250000   drop
0.09946289
8 1.03125000
-0.00328979		 1.03906250
0.02182474		 1.04687500   drop
0.04731979
9 1.03125000
-0.00328979		 1.03515625
0.00922009		 1.03906250   drop
0.02182474
10 1.03125000
-0.00328979		 1.03320312
0.00295332		 1.03515625   drop
0.00922009
11 1.03125000   drop
-0.00328979		 1.03222656
-0.00017119		 1.03320312
0.00295332
12 1.03222656
-0.00017119		 1.03271484
0.00139033		 1.03320312   drop
0.00295332
13 1.03222656
-0.00017119		 1.03247070
0.00060938		 1.03271484   drop
0.00139033
14 1.03222656
-0.00017119		 1.03234863
0.00021905		 1.03247070   drop
0.00060938
15 1.03222656
-0.00017119		 1.03228760
0.00002392		 1.03234863   drop
0.00021905
16 1.03222656   drop
-0.00017119		 1.03225708
-0.00007364		 1.03228760
0.00002392
17 1.03225708   drop
-0.00007364		 1.03227234
-0.00002486		 1.03228760
0.00002392
18 1.03227234   drop
-0.00002486		 1.03227997
-0.00000047		 1.03228760
0.00002392
19 1.03227997
-0.00000047		 1.03228378
0.00001172		 1.03228760   drop
0.00002392
20 1.03227997
-0.00000047		 1.03228188
0.00000563		 1.03228378   drop
0.00001172
21 1.03227997
-0.00000047		 1.03228092
0.00000258		 1.03228188   drop
0.00000563
22 1.03227997
-0.00000047		 1.03228045
0.00000105		 1.03228092   drop
0.00000258
23 1.03227997
-0.00000047		 1.03228021
0.00000029		 1.03228045   drop
0.00000105
24 1.03227997   drop
-0.00000047		 1.03228009
-0.00000009		 1.03228021
0.00000029
25 1.03228009
-0.00000009		 1.03228015
0.00000010		 1.03228021   drop
0.00000029
26 1.03228009
-0.00000009		 1.03228012
0.00000001		 1.03228015   drop
0.00000010
27 1.03228009   drop
-0.00000009		 1.03228010
-0.00000004		 1.03228012
0.00000001
28 1.03228010   drop
-0.00000004		 1.03228011
-0.00000002		 1.03228012
0.00000001
29 1.03228011   drop
-0.00000002		 1.03228011
-0.00000001		 1.03228012
0.00000001
30 1.03228011   drop
-0.00000001		 1.03228012
-0.00000000		 1.03228012
0.00000001
31 1.03228012
-0.00000000		 1.03228012
0.00000000		 1.03228012   drop
0.00000001