We introduce a novel shape-sensing method using Resistive Flex Sensors (RFS) embedded in cable-driven Continuum Dexterous Manipulators (CDMs). The RFS is predominantly sensitive to deformation rather than direct forces, making it a distinctive tool for shape sensing. The RFS unit we designed is a considerably less expensive and robust alternative, offering comparable accuracy and real-time performance to existing shape sensing methods used for the CDMs proposed for minimally-invasive surgery. Our design allows the RFS to move along and inside the CDM conforming to its curvature, offering the ability to capture resistance metrics from various bending positions without the need for elaborate sensor setups. The RFS unit is calibrated using an overhead camera and a ResNet machine learning framework. Experiments using a 3D printed prototype of the CDM achieved an average shape estimation error of 0.968 mm with a standard error of 0.275 mm. The response time of the model was approximately 1.16 ms, making real-time shape sensing feasible. While this preliminary study successfully showed the feasibility of our approach for C-shape CDM deformations with non-constant curvatures, we are currently extending the results to show the feasibility for adapting to more complex CDM configurations such as S-shape created in obstructed environments or in presence of the external forces.